The length of the latus rectum of the ellipse $4 x^{2} + 9 y^{2} = 1$ is..........

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Solution

Given equation of ellipse-
$4 x^{2} + 9 y^{2} = 36$
$\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$
Here $a = 3, b = 2$
Length of latus rectum $= \frac{2 b^{2}}{a} = \frac{2 \times {(2)}^{2}}{3} = \frac{8}{3}$

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The length of the latus rectum of the ellipse 4x2+9y2=1 is..........

Given equation of ellipse-4x2+9y2=36x29+y24=1Here a=3,b=2Length of latus rectum =2b2a=2×(2)23=83

The length of the latus rectum of the ellipse $4 x^{2} + 9 y^{2} = 1$ is..........

Given equation of ellipse-
$4 x^{2} + 9 y^{2} = 36$
$\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$
Here $a = 3, b = 2$
Length of latus rectum $= \frac{2 b^{2}}{a} = \frac{2 \times {(2)}^{2}}{3} = \frac{8}{3}$